From VASP Wiki

The Vienna ab-initio simulation package (VASP) is a computer program for atomic scale materials modeling, e.g., electronic-structure calculations and quantum-mechanical molecular dynamics, from first principles.

VASP computes an approximate solution to the many-body Schrödinger equation, either within density-functional theory (DFT), solving the Kohn-Sham (KS) equations, or within the Hartree-Fock (HF) approximation, solving the Roothaan equations. Hybrid functionals that mix the Hartree-Fock approach with density-functional theory are implemented as well. Furthermore, Green’s functions methods based on many-body perturbation theory are available in VASP. For instance, the GW method, random-phase approximation, 2nd-order Møller-Plesset, Bethe-Salpeter equations, and more.

In VASP, central quantities, like the one-electron orbitals, the electronic charge density, and the local potential are expressed in plane-wave basis sets. The interactions between the electrons and ions are described using norm-conserving or ultrasoft pseudopotentials, or the projector-augmented-wave method.

To determine the electronic ground state, VASP makes use of efficient iterative matrix diagonalization techniques, like the residual-minimization method with direct inversion of the iterative subspace (RMM-DIIS) or blocked Davidson algorithms. These are coupled with highly efficient Broyden and Pulay density mixing schemes to speed up the self-consistency cycle.